Hunger
Hunger is now a new feature in Minecraft which can get many people confused, and more likely to die from hunger (directly on Hard difficulty, indirectly on Normal and Easy difficulty) than from creepers. This is a tutorial to manage your hunger slightly carefully.
Food
Food is part of what you will need to survive. Food does not heal you directly, it only fills your hunger bar, which, when full, will heal you over time. However, you will start taking damage if you allow your hunger bar to be completely depleted. Different food items sate your hunger more or less effectively.
Cookies
Restores 
These are a very hard to craft(requiring very rare Cocoa Beans), food item. With 8 cookies created per crafting, these are not a very efficient food item. Filling up only half a bar on the hunger bar for each cookie consumed, a single craftings worth heals as much as a Cooked Porkchop. It is not recommended you use these, only keep them as little mementos.
Beef/Porkchop
Restores 
(raw) and (cooked)
Delicious and nutritious meat, this food item should be easy to get right off the bat, as Cows and Pigs roam everywhere. When cooked, the meat heals 4 units on the hunger bar. However, in already-generated chunks, animals spawn only rarely. Thus, meat should be used as food only occasionally. It is suggested that you start farming after the first few days.
Chicken
Restores (raw) and (cooked)
Another type of meat that can be obtained by killing chickens. When raw there is a chance that it can cause food poisoning, so it is recommended to cook it unless you really have no choice. It is fairly easy to get because chickens aren't rare animals and can easily be farmed with eggs.
Apple
Restores (red) and (golden)
Apples are a rare food item which appears in chests and oak tree leaves rarely when they are destroyed or decay. Golden apples may also be found in chests, and can be crafted using a red apple and eight golden nuggets. They also will accelerate your health regeneration for four seconds regardless of your whether or not hunger bar is full.
Bread
Restores
Bread is one of the most commonly used foods, and is also one of the most renewable. Easy to make, it is crafted from farmable wheat, four bread will fill one's hunger bar completely. Tall Grass needs to be harvested in order to obtain the seeds necessary for farming wheat.
Cake
Restores (per slice eaten, 6 slices total)
Cake is the only food that must be placed before eating. However, cake is harder to craft than most food items, requires three milk buckets and is not stackable in your inventory.
Fish
Restores (raw) and (cooked)
If you have access to water, fishing is a great way to gather food, and after it is cooked it heals 3 units on the hunger bar. After creating a fishing rod, a 4 block deep patch of water will provide an endless supply of food. Fish also has the benefit of being able to be harvested inside of your shelter by digging a hole and using a bucket to fill it with water.
Mushroom Stew
Restores
Fairly hard to get at first but easy to farm food, Mushroom Stew is quite affordable and hunger staving meal. It heals 4 units, like Steak, but it is quicker and less brutal to obtain. Mushroom Farms should be made in order to husband mushrooms wisely. Mushroom stew does not stack, however a Crafting Table is not required to craft the stew (one may keep ingredients in his inventory then craft it when needed).
Melon
Restores
Melon slice can be obtained by harvesting a Melon Block. Each slice heals 1 unit, but you should get a lot of them through Melon Farming. However, Abandoned Mineshafts hold the only way to obtain them, so keep a bucket of Milk with you when you're near a lot of Cobwebs to use if poisoned by a Cave Spider.